A duality and an analytic profile of topological entropy in percolation expressions of 2D Potts spin systems

By the Kasteleyn and Fortuin formulation, a Potts spin system can be expressed as a percolation system of spin clusters. The topological entropy can be defined from the number of spin cluster patterns as a function of the numbers of bonds and clusters. Using a self duality, the topological entropy i...

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Bibliographic Details
Published in:Journal of the Physical Society of Japan 1999-10, Vol.68 (10), p.3307-3314
Main Authors: KASAI, Y, IKEDA, H, NOMURA, S, OHNAKA, K
Format: Article
Language:English
Subjects:
Condensed matter: electronic structure, electrical, magnetic, and optical properties
Critical-point effects, specific heats, short-range order
Dynamic properties (dynamic susceptibility, spin waves, spin diffusion, dynamic scaling, etc.)
Exact sciences and technology
Lattice theory and statistics (ising, potts, etc.)
Magnetic properties and materials
Phase transitions: general studies
Physics
Statistical physics, thermodynamics, and nonlinear dynamical systems
Thermodynamics
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Summary:By the Kasteleyn and Fortuin formulation, a Potts spin system can be expressed as a percolation system of spin clusters. The topological entropy can be defined from the number of spin cluster patterns as a function of the numbers of bonds and clusters. Using a self duality, the topological entropy is shown to have the maximum value at the transition temperature for the square lattice. It also shows a delicate singular structure around the transition point even at the unity degree of internal freedom, the one-state Potts model, as a unified generating function. The strongly-frustrated Ising system is understood as the one-state Potts model with the real spin clusters.
ISSN:0031-9015
1347-4073
DOI:10.1143/jpsj.68.3307